Sentence examples for normalized norm from inspiring English sources
A simple example of absolute normalized norm is usual l r (1 ≤ r ≤ ∞) norm.
A simple example of absolute normalized norm is usual l p (1 ≤ p ≤ ∞) norm.
Later, Guliyev [5] defined the generalized Morrey spaces (M_{p,varphi}) with normalized norm.
It follows that is isometrically isomorphic to (ℝ2, |.|) and |.| is an absolute and normalized norm, and the corresponding convex function is given by.
The approach extends the standard SIMP method by including the normalized norm of the spatial gradient of the design field into the material interpolation function, enforcing coating material at interfaces by attributing particular properties.
ψ * is an absolute normalized norm and the corresponding convex function ψ* ∈ Ψ is ψ * ( t ) = sup 0 ≤ s ≤ 1 ( 1 - s ) ( 1 - t ) + s t ψ ( s ). for t with 0 ≤ t ≤ 1.
We introduce a new class of normalized norms on which properly contains all absolute normalized norms.
We now consider the Ptolemy constant of a class of absolute normalized norms on ℝ2.
We now consider the constant J X, p (1) of a class of absolute normalized norms on ℝ2.
The set of all absolute normalized norms on R 2 is denoted by A N 2. Bonsall and Duncan [1] showed the following characterization of absolute normalized norms on R 2. Namely, the set A N 2 of all absolute normalized norms on R 2 is in a one-to-one correspondence with the set Ψ 2 of all convex functions ψ on [ 0, 1 ] satisfying max { 1 − t, t } ≤ ψ ( t ) ≤ 1 for all t ∈ [ 0, 1 ] (cf. [2]).
In this section, we give a simple method to determine and estimate the constant J X, p (1) of absolute normalized norms on ℝ2.
